How Can You Effectively Visualize and Draw Vector Fields?

[sandy.bridge]

Hello all,
Just looking for tips on "visualizing" vector fields and perhaps drawing them. I have encountered a few that have given me trouble.
As an example,
$$\vec{F}(x, y)=[cos(y), -cos(x)]$$
Applying $dx/F_1=dy/F_2$ I get,
$$sin(x)+sin(y)=C$$
I have also seen what the vector field looks like, but I am wondering if there are any techniques for questions like these.

 

[lavinia]

Hello all,
Just looking for tips on "visualizing" vector fields and perhaps drawing them. I have encountered a few that have given me trouble.
As an example,
$$\vec{F}(x, y)=[cos(y), -cos(x)]$$
Applying $dx/F_1=dy/F_2$ I get,
$$sin(x)+sin(y)=C$$
I have also seen what the vector field looks like, but I am wondering if there are any techniques for questions like these.

one way to visualize vector fields is to draw their integral curves, the curves c(t) such that c'(t) = F